ABC

Algebra Level 1

Find a , b , c a, b, c which are real numbers that satisfy

a 2 + b 2 + c 2 = 0. { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }=0.

0,1,0 -1,0,1 0,0,0 1,0,-1

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16 solutions

Victor Loh
Jun 28, 2014

The square of a real number is non-negative. Hence a 2 = b 2 = c 2 = 0 ( a , b , c ) = ( 0 , 0 , 0 ) a^{2}=b^{2}=c^{2}=0\implies (a,b,c)=\boxed{(0,0,0)} and we are done.

Did he have to give it as an MCQ question? Way too easy.

Joshua Ong - 6 years, 11 months ago

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Exactly! He could have asked for like a + b + c a+b+c or something. :P

Finn Hulse - 6 years, 11 months ago

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https://brilliant.org/problems/1234/

Rohan Karmakar - 5 years, 2 months ago

whyy??? invisibLe by 1 right??? so it is (1,1,1)

Christian Dialino - 6 years, 8 months ago
Anish Gupta
Jul 11, 2014

Square of a real number is always Non negative i.e. ( 1 ) 2 = 1 (-1)^{2} = 1 ( 2 ) 2 = 4 (-2)^{2} = 4 ( 0.5 ) 2 = 0.25 (-0.5)^{2} = 0.25 ( 0 ) 2 = 0 (0)^{2} = 0

so the sum of 3 non negative is equal to zero only when each number is equal to zero

a 2 = b 2 = c 2 = 0 a^{2} = b^{2} = c^{2} = 0 implies ( a , b , c ) = ( 0 , 0 , 0 ) (a,b,c) = (0,0,0)

Thanks to clear my doubt

abudahir 617 - 5 years, 7 months ago

Zero squared= 1 so this whole question is wrong

Josh Murley - 6 years, 1 month ago

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0^2=0×0=0 not 1 You might be confusing this for 0! Which is equal to 1 or 0^0 which is not defined.

Sonali Sinha - 5 years, 11 months ago

You are right! This question is impossible to solve. Zero squared is equal 1. No answer given satisfy this condition.

Cezário Abrantes - 6 years ago

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no, 0^x=0, x^0=1

Nota Xue - 5 years, 9 months ago

0 squared means 0x0 And I think that you know 0x0 so how can you say that 0 squared is 1

Sonal Singh - 5 years, 9 months ago

I agree zero to any power is 1. The whole question is invalid.

Jessica Beck - 5 years, 9 months ago

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@Jessica Beck No absolutely not, the questions is valid in 0^2=0

Jan Grünwaldt - 5 years, 5 months ago
Reeshabh Ranjan
Jul 8, 2014

Something is wrong, they said a,b and c are real numbers [only positive], so how come they all can be zero ?

Real numbers can be positive, negative, or 0 0 .

Daniel Liu - 6 years, 11 months ago

If the author was looking for positive real numbers, he would be asking for 'positive reals'.

Victor Loh - 6 years, 11 months ago
Adarsh Pankaj
Jan 14, 2016

Square of a real number is always positive. Thus, if 3 positive integers add up to zero there is only one possibility that all the numbers are zeroes.

Reuben Mark Elias
Nov 19, 2015

It's not defined because a,b,c are different variables, they have different values. They can't be 0,0,0

Senthamil Arasi
Aug 20, 2015

a=0 b=0 c=0 0^2=0 zero squre values of also calculate zero ( a b c)=(0 0 0)

the answer is 0 0 0

Samir Shaheen
Jul 25, 2015

It can be also that at least one of the a or b or c is a complex number. This will give a negative value that will get the 0.

Nushrat Naushin
Jun 14, 2015

if we square any positive or negative number, we will get a positive answer.For example, (1)^2=1 and (-1)^2=1.So, we can never get a negative answer by squaring something. The only way to satisfy the equation is when all a,b,c are equal to zero.,

since 0 square is equivalent to 0, hence all variables should be zero and not 1 whose square is still 1

Liji Kj
Jan 6, 2015

a^2+b^2+c^2=0 ,a=b=c=0

Deepthi Prakash
Aug 3, 2014

0squ.+0squ.+osqu=0 n ans 0,0,0

Hassan Raza
Jul 30, 2014

( 0 , 0 , 0 ) i s r i g h t a n s w e r B e c a u s e 0 2 + 0 2 + 0 2 = 0 o t h e r s a r e i n c o r r e c t (0,0,0)\quad is\quad right\quad answer\\ Because\\ { 0 }^{ 2 }{ +0 }^{ 2 }{ +0 }^{ 2 }=0\\ others\quad are\quad incorrect

Pankaj Nirwan
Jul 14, 2014

It is very easy ; since , a.a + b.b + c.c =0 { says equation 1 } by equation 1 we have , a.a = b.b = c.c = 0

so ; ( a,b,c ) = ( 0,0,0 ) .

Satvik Mashkaria
Jul 8, 2014

since sqare of real numbers ae always non-negative,if sum of three non-negative numbers are 0 then they must be 0.

Prince Mishra
Jul 8, 2014

in all option only this option is having real number so ans is 0,0,0

Vineet Patel
Jul 7, 2014

-1 square will give you +1 so only one possibility i.e. 0 0 0

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